Internal problem ID [9843]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1518.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) x y^{\prime \prime \prime }+3 \left (2 x^{2}+1\right ) y^{\prime \prime }-12 y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 60
dsolve((x^2+1)*x*diff(diff(diff(y(x),x),x),x)+3*(2*x^2+1)*diff(diff(y(x),x),x)-12*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 \,\operatorname {arctanh}\left (\frac {1}{\sqrt {x^{2}+1}}\right ) \sqrt {x^{2}+1}\, c_{2} x^{2}+c_{1} \sqrt {x^{2}+1}\, x^{2}+2 c_{3} x^{3}-3 c_{2} x^{2}+c_{3} x -c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.483 (sec). Leaf size: 69
DSolve[-12*y[x] + 3*(1 + 2*x^2)*y''[x] + x*(1 + x^2)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} \left (-3 c_3 x \sqrt {x^2+1} \text {arctanh}\left (\sqrt {x^2+1}\right )+c_1 \left (4 x^2+2\right )+2 c_2 x \sqrt {x^2+1}+3 c_3 x+\frac {c_3}{x}\right ) \]